# Control refinement for discrete-time descriptor systems: a behavioural approach via simulation relations

## TL;DR

This paper introduces a behavioural approach to control refinement for discrete-time descriptor systems, enabling analysis and control design on reduced-order models despite algebraic couplings.

## Contribution

It extends hierarchical control refinement to descriptor systems with algebraic couplings using simulation relations within the behavioural framework.

## Key findings

- Enables control analysis on reduced-order descriptor models
- Handles algebraic couplings in descriptor systems
- Extends hierarchical control refinement methods

## Abstract

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement notion for these descriptor systems that enables analysis and control design over related reduced-order systems. Utilising the behavioural framework, we extend upon the standard hierarchical control refinement for ordinary systems and allow for algebraic couplings inherent to descriptor systems.